I am teaching myself mathematics, my objective being a thorough understanding of game theory and probability. In particular, I want to be able to go through A Course in Game Theory by Osborne and Probability Theory by Jaynes.
I understand I want to cover a lot of ground so I'm not expecting to learn it in less than a year or maybe even two. Still I'm fairly certain it's not impossible.
However I would like to have a study plan more or less fleshed out just to know I'm on the right track. There were some other questions related to self learning math here but I couldn't find one like mine.
I'd appreciate some feedback.
Calc I + II: no book, I already know basic calculus
- Differential equations: MIT's OCW lectures
- Calc III: Stewart's Multivariable calculus
- Linear Algebra: Strang, Gilbert, Linear Algebra and Its Applications complemented with MIT's OCW lectures OR Linear Algebra Done Right
Until here I am more or less certain on what I want to study, but I'm totally confused on what to learn next. Jayne's book states that you need to be familiar with applied mathematics.
After reading about applied mathematics, I came up with this plan to be done after finishing what I mentioned earlier (in order of course, not all at the same time):
- Topology A: Munkres, part I.
- Real analysis: Still not sure about the material, probably Abbott or Rudin.
- Complex Analysis: No idea about the material
- Group Theory: Rotman, An Introduction to the Theory of Groups
- Topology B: Munkres, part II.
And then finally, Jayne's Probability Theory and game theory.
Am I missing something here? Some of these books such as Rotman's are aimed at a graduate level, is it foolish to think I will understand them?